Energy in car physics question

Question

A driver carelessly ignores the posted speed limit of 40.0 km/h in a school zone and continues at 65 km/h. Assuming a good reaction time of 0.80 s, using the concept of energy how many more meters will it take him to stop than if he had reduced his speed? Assume a constant emergency braking acceleration of –7.8 m/s².

Answer 1

Answer: 18.5 meters

Explanation:

First we need to find out how long the car will be traveling in both examples

V_f = V_i + at

Final velocity = Initial Velocity + acceleration * time

Since we want final velocity to be 0, we have

V_i + at = 0

Now we isolate time since that's what we want to solve for

t = V_i / a

Now we simply plug in our two examples and compare results after fixing the units.

40 km/h = 11.11 m/s

65 km/h = 18.06 m/s

t = 11.11 m/s / -7.8 m/s² = 1.42 seconds

t = 18.06 m/s / -7.8 m/s² = 2.31 seconds

Now that we know how long it takes to stop, we can find out the total displacement during that period.

s = vt + (1/2) at²

s = 11.11(1.42) + (1/2) (-7.8) (1.42)² = 7.91 meters

s = 18.06(2.31) + (1/2)(-7.8)(2.31)² = 20.90 meters

Now we simply have to add in the distance traveled during the reaction time before breaking starts

11.11*(0.80) = 8.89 meters

18.06 *(0.80) = 14.44 meters

7.91 meters + 8.89 meters = 16.80 meters until stopped

20.90 meters + 14.44 meters = 35.34 meters until stopped

Finally we find the difference between the two

35.3 - 16.8 = 18.5 meters

Over twice the distance!